Many things will probably change in the upcoming sequel to The Legend of Zelda: Breath of the Wild, tentatively referred to as Breath of the Wild 2, and a big one is Link's Champion Abilities that he gets after clearing each of the four Divine Beasts. So far, they haven't even been confirmed to return, but since BOTW's four champions, how they died, and their abilities are major elements of the story, they are likely to come back in some form or another. BOTW 2 is currently set to release sometime in Spring 2023, so it may be awhile before news of how it will use the Champion Abilities comes.
In Breath of the Wild, there were four Champions of Hyrule who lived before the Second Great Calamity, each from a different race and possessing a special power. They piloted the Divine Beasts, with plans to use them against Calamity Ganon, but sadly lost their lives fighting monsters that he sent to corrupt them. Once Link defeats these monsters and reclaims their Divine Beast, the Champions will appear in the form of spirits and bestow their powers unto him. Link is able to utilize each of BOTW's four Champions' best strengths throughout his adventures in Hyrule, though they have cooldown periods before they can be activated again.
The four Champion Abilities are only one thing that could change in BOTW 2, but it's one that could have a big impact. How they would change is almost impossible to predict, but the idea of being able to use different forms of powers like Urbosa's Fury and Revali's Gale is quite exciting. It's even possible that BOTW 2 will completely discard them and replace them with something else. Hopefully, any change or replacement would only be an improvement, and players will enjoy using them once BOTW 2 comes out.
Will Champion Abilities Appear In Breath of the Wild's Sequel?
If BOTW 2 includes the Champion Abilities, it's unlikely that they'll be available right at the start of the game due to how strong and useful they are in terms of both exploration and combat in BOTW. Nintendo almost always changes things from game to game, and having them return in their original forms could be repetitive and stale, so that also doesn't seem probable. They can still appear in some form, however, especially if the Champions or their spirits also make another appearance.
Link probably wouldn't obtain the abilities in BOTW 2 by clearing the Divine Beasts like he did in the original game if they make a return. Despite BOTW's open-world format that allows players to go directly to the final boss battle against Calamity Ganon without doing any missions right after finishing the tutorial if they'd like, it can be reasonably assumed that the main story missions at the bare minimum were completed in BOTW's continuity, especially the ones that involve Link saving his friends from Ganon's clutches. Therefore, Link most likely already reclaimed Zelda: BOTW's Divine Beasts like Vah Rudania before the events of BOTW 2, and shouldn't have to do so again.
How Zelda: Breath of the Wild 2 Can Use The Champion Abilities
There are a few different ways that BOTW 2 could change the Champion Abilities and how Link obtains them. It's possible that he'll learn them in a series of missions that involve studying the Champions' pasts and any journals they may have left behind, or from the new Champions that aided him in reclaiming the Divine Beasts; Sidon, Yunobo, Riju, and Teba. Yunobo already possesses Daruk's Protection, so this is quite feasible. Why he would need to relearn them and how he lost them in the first place is another interesting question. It's possible that they faded when Link defeated Ganon, or when the original Champions' spirits fully passed on.
When he obtains the Champion Abilities again, BOTW 2 can let Link use them in new ways. Link could make his own techniques based on them, that are perhaps weaker but more easily-usable, and require shorter cooldowns or even none at all. He could also combine them, and create electrically-charged shields with Daruk's Protection and Urbosa's Fury, for example, or waterspouts with Mipha's Grace and Revali's Gale. Other possibilities include having them start out weak but be able to be upgraded into powers stronger than their original forms, being tied to the Champions' weapons - which could go a long way towards making them more viable - and crafting consumable items based on them that have the same effects.
What BOTW 2 Could Use Instead Of The Champion Abilities
There's also the possibility that the Champion Abilities won't return in BOTW 2, in which case something else could be used to fill the void. Link could obtain new powers from the goddess Hylia, who created the Zelda series' most powerful weapon, the Master Sword, or from the three dragons - Farosh, Dinraal, and Naydra - that roam BOTW's Hyrule. There are also other sources that Link could obtain new powers to replace the Champions' Abilities from, such as the Sheikah tribe in Kakariko Village, or the Koroks and Great Deku Tree that resides in the Korok Forest.
Each of these could take the form of combat or exploration powers, just as the Champions' Abilities do; a Korok or Great Deku Tree power could create a platform or bridge made of roots for example, which could come in handy greatly since Link will be exploring floating islands. Powers from the dragons could take the form of fire, ice, and lightning attacks, though the likelihood of this is uncertain since swords, spears, and wands with these elements are in BOTW, weapons that might reappear in BOTW 2, and the powers may make such items redundant.
BOTW 2 has actually shown a few of the new abilities that Link will use, along with the possible source; in one of the first teaser trailers from Nintendo on YouTube, Link is shown using some sort of power that lets him phase through solid matter, which could be a good exploration power to use in lieu of Revali's Gale. This presumably comes from Link's new arm since the same glow that surrounds it is the same one that appears when he uses the phasing ability. It could be a good source for new powers to replace the Champion Abilities, and the possibility introduces some weird theories about Link's BOTW 2 arm. Since that arm is the same one that's engulfed in Ganon's Malice, it could even be an indication that these powers will come from a dark source such as Calamity Ganon, Ganondorf, or Demise. Demise's spirit is sealed within the Master Sword, which is damaged in Nintendo's Launch Timing Update - also on YouTube - so it's not outside the realm of possibility that he will return in The Legend of Zelda: Breath of the Wild 2, and is sealed within Link's new arm or inhabiting it somehow.
Sources: Nintendo/YouTube (2021 Teaser), Nintendo/YouTube (Launch Timing Update)